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At least 379 records · Page 21

Description of SAFIRE for ISES

The SAFIRE (Spectroscopy of the Atmosphere using Far Infrared Emission) is a limb emission experiment using a far-IR Fourier transform spectrometer (FTS) and a mid-IR broadband multispectral radiometer covering the range 80 to 1600/cm. The purpose of this experiment is to obtain vertical distributions of temperature and key constituents of O(y), HO(y), NO(y), ClO(y), and BrO(y) families in the stratosphere, mesosphere, and thermosphere. The spectral channels and gases within each channel are summarized. The instrument includes a 48 element (6 x 8) Ge:GA detector array operating at 4 K in the far-IR and a 105 element (7 x 15) HgCdTe array operating at 80 K in the mid-IR. The SAFIRE uses four different scan modes for vertical coverage and resolution to address various scientific requirements. The SAFIRE data reduction will start with the retrieval of temperature profile as a function of pressure using two CO2 channel data. Constituent distributions then are obtained from other channel data using the retrieved temperature profile. The SAFIRE measurements are limited to the region above the tropopause because of radiance saturation by H2O and clouds. The computational capability necessary to process at the instrument data rate is estimated to be 19 MFLOPS for FTS data and 0.02 MFLOPS for radiometer data. It seems, therefore, that the real-time applications of SAFIRE data using an onboard processing device is not feasible. Although a temperature anomaly may be detected from the two CO2 radiometer channels using an onboard processor for the stratosphere, it is not possible to distinguish between CO2 outflux and temperature anomaly. Temperature anomaly does not, therefore, offer tropospheric information useful for real-time application.

Park, Jae H.↗

Formation of a Tropopause Cirrus Layer Observed over Florida during CRYSTAL-FACE

On July 13, 2002 a widespread, subvisible tropopause cirrus layer occurred over the Florida region. This cloud was observed in great detail with the NASA Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) instrumentation, including in situ measurements with the WB-57 aircraft. In this paper, we use the 13 July cloud as a case study to evaluate the physical processes controlling the formation and evolution of tropopause cirrus layers. Microphysics measurements indicate that ice crystal diameters in the cloud layer ranged from about 7 to 50 microns, and the peak number mode was about 10-25 microns. In situ water vapor and temperature measurements in the cloud indicated supersaturation with respect to ice throughout, with ice saturation ratios as large as 1.8. Even when the ice surface area density was as high as about 500 sq microns/cu cm, ice supersaturations of 20-30% were observed. Trajectory analysis shows that the air sampled near the tropopause on this day generally came from the north and cooled considerably during the previous few days. Examination of infrared satellite imagery along air parcel back trajectories from the WB-57 flight track indicates that the tropopause cloud layer formation was, in general, not simply left over ice from recently generated anvil cirrus. Simulations of cloud formation using time-height curtains of temperature along the trajectory paths show that the cloud could have formed in situ near the tropopause as the air was advected into the south Florida region and cooled to unusually low temperatures. If we assume a high threshold for ice nucleation via homogeneous freezing of aqueous sulfate aerosols, the model reproduces the observed cloud structure, ice crystal size distributions, and ice supersaturation statistics. Inclusion of observed gravity wave temperature perturbations in the simulations is essential to reproduce the observed cloud properties. Without waves, crystal number densities are too low, crystal sizes are too large, and the crystals fall out too fast, leaving very little cloud persisting at the end of the simulations. In the cloud simulations, coincidence of high supersaturations and high surface areas can be produced by either recent nucleation or sedimentation of crystals into supersaturated layers. The agreement between model results and observed supersaturations is improved somewhat if we assume that the steady state relative humidity within cirrus at T<200 K is enhanced by about 30%. The WB-57 measurements and the model results suggest that the cloud layer irreversibly dehydrated air near the tropopause.

Jensen, Eric↗

Real time acousto-ultrasonic NDE technique for monitoring damage in ceramic composites under dynamic loads

Research effort was directed towards developing a near real-time, acousto-ultrasonic (AU), nondestructive evaluation (NDE) tool to study the failure mechanisms of ceramic composites. Progression of damage is monitored in real-time by observing the changes in the received AU signal during the actual test. During the real-time AU test, the AU signals are generated and received by the AU transducers attached to the specimen while it is being subjected to increasing quasi-static loads or cyclic loads (10 Hz, R = 1.0). The received AU signals for 64 successive pulses were gated in the time domain (T = 40.96 micro sec) and then averaged every second over ten load cycles and stored in a computer file during fatigue tests. These averaged gated signals are representative of the damage state of the specimen at that point of its fatigue life. This is also the first major attempt in the development and application of real-time AU for continuously monitoring damage accumulation during fatigue without interrupting the test. The present work has verified the capability of the AU technique to assess the damage state in silicon carbide/calcium aluminosilicate (SiC/CAS) and silicon carbide/ magnesium aluminosilicate (SiC/MAS) ceramic composites. Continuous monitoring of damage initiation and progression under quasi-static ramp loading in tension to failure of unidirectional and cross-ply SiC/CAS and quasi-isotropic SiC/MAS ceramic composite specimens at room temperature was accomplished using near real-time AU parameters. The AU technique was shown to be able to detect the stress levels for the onset and saturation of matrix cracks, respectively. The critical cracking stress level is used as a design stress for brittle matrix composites operating at elevated temperatures. The AU technique has found that the critical cracking stress level is 10-15% below the level presently obtained for design purposes from analytical models. An acousto-ultrasonic stress-strain response (AUSSR) model for unidirectional and cross-ply ceramic composites was formulated. The AUSSR model predicts the strain response to increasing stress levels using real-time AU data and classical laminated plate theory. The Weibull parameters of the AUSSR model are used to calculate the design stress for thermo-structural applications. Real-time AU together with the AUSSR model was used to study the failure mechanisms of SiC/CAS ceramic composites under static and fatigue loading. An S-N curve was generated for a cross-ply SiC/CAS ceramic composite material. The AU results are corroborated and complemented by other NDE techniques, namely, in-situ optical microscope video recordings and edge replication.

Tiwari, Anil↗

Sulfide and sulfate saturation in hydrous silicate melts

A series of hydrothermal experiments was performed over a wide range of pressures, temperatures, oxygen fugacities, and melt FeO content, in order to examine the effects of physical changes on sulfur solubility in fractionated hydrous silicate melts. On the basis of the experimental results, it is concluded that upper crustal oxidation-reduction reactions and crystal fractionation processes may exert considerable influence on the amount of sulfur contained in magmas erupted at the surface. The application of the experimental results to investigations of volatile transport and volcanic degassing processes on the earth, Venus, and Mars is discussed

Carroll, M. R.↗

Using Wind and Temperature Fields to Study Dehydration Mechanisms in the Tropical Tropopause Layer

The tropics are the main region for troposphere-to-stratosphere transport (TST) of air. One of the dominant mechanisms that control tropical TST of water vapor is freeze-drying by the cold tropical tropopause. This mechanism is supported by evidence from satellite observations of the "tape recorder", where seasonal changes in stratospheric water vapor are in phase with seasonal changes in tropopause temperatures in the tropics. Over the last few years, however, the concept of the tropical tropopause has evolved from a single material surface to a layer called the Tropical Tropopause Layer (TTL). A recent hypothesis on dehydration mechanisms suggests that dehydration and entry point into the stratosphere are not always co-located (Holton and Gettelman, 2001). Instead, dehydration can occur during horizontal advection through Lagrangian 'cold pools', or coldest regions along a parcel's trajectory, as air ascends within the TTL while the entry point into the stratosphere occurs at a different geographical location. In this study, we investigate the impact that these Lagrangian cold pools have on TTL moisture. For this purpose, we use in situ measurements of TTL water vapor obtained aboard NASA's WB-57 aircraft over the Eastern Tropical Pacific, and we compare these measurements to minimum saturation water vapor mixing ratios obtained from three-dimensional backward trajectory calculations. Aircraft measurements show frequent unsaturated conditions, which suggest that the entry value of stratospheric water vapor in this region was not set by local saturation conditions. Trajectory calculations, driven by both ECMWF operational analysis and reanalysis winds and temperature fields, are used to explore the impact (e.g., geographical location, timing, dehydration magnitude) of the Lagrangian cold pools intercepted by the parcels sampled by the aircraft. We find noteworthy differences in the location of the Lagrangian cold pools using the two ECMWF data sets, namely influence of the Western Tropical Pacific region when using operational analysis fields versus influence of the Eastern Tropical Pacific and South America regions when using reanalysis fields. These results have a significant impact on our scientific conclusions on dehydration mechanisms affecting the air sampled by the aircraft, given that these regions have different thermodynamic and convective properties.

Pittman, Jasna↗

Using Si Diodes To Detect H2 Liquid/Vapor Interfaces

Commercially available silicon-diode temperature sensors used to detect interfaces between hydrogen liquid and hydrogen vapor at steady-state saturation conditions. Sensors mounted at short intervals along rod to form rake-like array. Array inserted in tank with rod oriented vertically, where it senses level of liquid hydrogen to resolution equal to interval between sensors. Basic idea to measure voltage across sensor while supplying small electric current that heats sensor. Because vapor cools sensor less effectively than liquid does, sensor's steady-state temperature greater when sensor surrounded by vapor than when immersed in liquid. Voltage output decreases as temperature increases for silicon diodes. Thus, temperature (voltage) reading used to determine whether liquid level above or below sensor.

Dempsey, Paula Jean↗

Maximum two-phase flow rates of subcooled nitrogen through a sharp-edged orifice

Data are presented of an experiment in which subcooled liquid nitrogen was discharged through a sharp-edged orifice at flow rates near the maximum. The data covered a range of inlet stagnation pressures from slightly above saturation to twice the thermodynamic critical pressure. The data were taken along five separate inlet stagnation isotherms ranging from 0.75 to 1.035 times the thermodynamic critical temperature. The results indicate that subcooled liquids do not choke or approach maximum flow in an asymptotic manner even though the back pressure is well below saturation; and orifice flow coefficients are not constant as is frequently assumed. A metastable jet appears to exist which breaks down if the difference between back pressure and saturation pressure is large enough.

Simoneau, R. J.↗

Scintillations during occultations by planets. I - An approximate theory

Fluctuations are observed during occultations of both stars and spacecraft by planetary atmospheres. Existing treatments of spacecraft scintillations ignore a major effect unique to occultations: the severe flattening of the Fresnel zone or source image by defocusing. Other large effects, due to 'saturation' of the scintillation, have also been ignored. The deeper portions of atmospheric temperature and density profiles inferred from occultation data are seriously in error if other planets' atmospheres are as turbulent as our own. Thus, profiles obtained from entry probes (e.g., the Soviet Venera series) are probably more accurate than those from radio occultation (Mariner 5 and 10) data. Scintillation greatly reduces the information obtainable from occultation observations; much of the detail attributed to layering in published profiles is probably due to aliasing of turbulence. This paper gives an approximately correct theoretical treatment that is a substantial improvement over published theories, and shows how a more accurate theory could be constructed. Some methods for a more accurate determination of atmospheric structure are proposed.

Young, A. T.↗

Mars - A contamination potential?

Three regions on Mars, Solis Lacus, Noachis-Hellespontus, and the Syrtis Major border areas, would appear to have generally less hostile environments than at the Viking lander sites. Significant soil moisture may extend to within about 1 cm of the surface. Water vapor pressures within the pore spaces may be near saturation, and brines may be physically segregated from pockets of relatively pure H2O. Temperatures reach above 0 C during southern spring and summer, with peak temperatures reaching +22 C. These regions should contain fewer oxidants, and primary synthesis of organics may occur. The potential for contamination of these sites by microbes transported from existing spacecraft should be assessed. The adequacy of proposed new planetary protection procedures for possible future United States Mars Surface Sample Return missions should also be assessed in light of these findings.

Huguenin, R. L.↗

Characterization of LANDSAT-4 TM and MSS Image Quality for Interpretation of Agricultural and Forest Resources

Systematic analysis of both image and numeric data shows that the overall spectral, spatial, and radiometric quality of the TM data are excellent. Spectral variations in fallow fields are due to the vaiability in soil moisture and surface roughness resulting from the various stages of field preparation for small grains production. Spectrally, the addition of the first TM short wave infrared band (Band 5) significantly enhanced ability to discriminate different crop types. Bands 1, 5, and 6 contain saturated pixels due to high albedo effects, low moisture conditions, and high radiant temperatures of granite and dry, bare soil on south facing slopes, respectively. Spatially, the two fold decrease in interpixel distance and four fold decrease in area per pixel between the TM and MSS allow for improved discrimination of small fields, boundary conditions, road and stream networks in rough terrain, and small forest clearings resulting from various forest management practices.

Degloria, S. D.↗

Remanent magnetization of a 'paramagnetic' composition in the ilmenite-hematite solid solution stress

In the ilmenite-hematite solid solution series, compositions more ilmenite-rich than Ilm(73)Hem(27) are classically thought to be paramagnetic at room temperature. Ilm(80)Hem(20) samples have nevertheless been synthesized that acquire hard saturation remanent and thermoremanent moments. From analysis of AC demagnetization data, the source of the measured remanence is believed to be a single-domain (SD) like material within the IlM(80)Hem(20) grains themselves. On the basis of transmission electron microscope observations, it is suggested that transformation-induced domain boundaries, which in part are enriched in hematite component relative to the bulk composition of the grains, could act as the magnetic carrier of the SD-like remanence.

Lawson, C. A.↗

Solution and shock-induced exsolution of argon in vitreous carbon

To add to the knowledge of noble gas solution and exsolution in carbonaceus material, experiments were performed on vitreous carbon. Ar-rich vitreous carbon samples were prepared under vapor-saturated conditions using argon as the pressurizing medium. Solubility data were obtained for temperatures of 773 to 973 K and pressures of 250 to 1500 bars. Up to 7 wt pct Ar was dissolved in the carbon. The solubility data were compared to a thermodynamic model of argon atoms dissolving into a fixed population of 'holes' in the carbon. Two variations of the model yielded estimates of the enthalpy of solution of Ar in vitreous carbon equal to about -4700 cal/mole. Preliminary shock experiments showed that 28 percent of the total argon was released by driving 4 GPa shocks into the argon-rich carbon. It was demonstrated that shock-induced argon loss is not simply caused by the impact-induced diminution of grain size. The present value of shock pressure required for partial impact devolatilization of Ar from carbon is below the range (5-30 GPa) at which H2O is released from phyllosilicates.

Gazis, Carey↗

A Proposal for an Integrated Geophysical Strategy to "Follow the Water" on Mars

The search for subsurface water has become a primary focus of Mars exploration. Its abundance and distribution (both as ground ice and groundwater) have important implications for understanding the geologic, hydrologic, and climatic evolution of the planet; the potential origin and continued survival of life; and the accessibility of a critical in situ resource for sustaining future human explorers. For these reasons, a principal goal of the Mars science, astrobiology, and the HEDS programs is to determine the 3-D distribution and state of subsurface H2O, at a resolution sufficient to permit reaching any desired volatile target by drilling. The three targets most often discussed are: groundwater, massive deposits of near-surface ground ice (associated with the ponded discharge of the outflow channels or the relic of a former ocean), and ice-saturated frozen ground. Based on the present best estimates of mean annual surface temperature, crustal thermal conductivity, geothermal heat flow, and groundwater freezing temperature, the mean thickness of frozen ground on Mars is expected to vary from approx. = 2.5 - 5 km at the equator to approx. = 6.5 - 13 km at the poles. However, natural variations in both crustal heat flow and thermal conductivity are likely to result in significant local departures from these predicted values. The recent discovery of "young" fluvial-like features, emanating from the slopes of local scarps, raises the possibility that liquid water may also exist episodically at shallow (approx. = 100 - 500 m) depth; however, the true nature and absolute age of these features remains highly uncertain. Although the belief that Mars is water-rich is supported by a wide variety geologic evidence, our ignorance about the heterogeneous nature and thermal evolution of the planet's crust effectively precludes geomorphic or theoretical attempts to quantitatively assess the current geographic and subsurface vertical distribution of ground ice and groundwater . For this reason, any exploration activity (such as drilling) whose success is contingent on the presence of subsurface water, must be preceded by a comprehensive high-resolution geophysical survey capable of assessing whether local reservoirs of water and ice actually exist. Terrestrial experience has demonstrated that the accurate identification of such targets is likely to require the application of multiple geophysical techniques. In this abstract we propose an integrated strategy for the geophysical exploration of Mars that we believe represents the fastest, most cost-effect, and technically capable approach to identifying the state and distribution of subsurface water. Additional information is contained in the original extended abstract.

Clifford, S. M.↗

Hydrogen in rocks: an energy source for deep microbial communities

To survive in deep subsurface environments, lithotrophic microbial communities require a sustainable energy source such as hydrogen. Though H2 can be produced when water reacts with fresh mineral surfaces and oxidizes ferrous iron, this reaction is unreliable since it depends upon the exposure of fresh rock surfaces via the episodic opening of cracks and fissures. A more reliable and potentially more voluminous H2 source exists in nominally anhydrous minerals of igneous and metamorphic rocks. Our experimental results indicate that H2 molecules can be derived from small amounts of H2O dissolved in minerals in the form of hydroxyl, OH- or O3Si-OH, whenever such minerals crystallized in an H2O-laden environment. Two types of experiments were conducted. Single crystal fracture experiments indicated that hydroxyl pairs undergo an in situ redox conversion to H2 molecules plus peroxy links, O3Si/OO\SiO3. While the peroxy links become part of the mineral structure, the H2 molecules diffused out of the freshly fractured mineral surfaces. If such a mechanism occurred in natural settings, the entire rock column would become a volume source of H2. Crushing experiments to facilitate the outdiffusion of H2 were conducted with common crustal igneous rocks such as granite, andesite, and labradorite. At least 70 nmol of H2/g diffused out of coarsely crushed andesite, equivalent at standard pressure and temperature to 5,000 cm3 of H2/m3 of rock. In the water-saturated, biologically relevant upper portion of the rock column, the diffusion of H2 out of the minerals will be buffered by H2 saturation of the intergranular water film.

Hydrogen/analysis↗

Amino Acid Degradation after Meteoritic Impact Simulation

Amino acids are among the most important prebiotic molecules as it is from these precursors that the building blocks of life were formed [1]. Although organic molecules were among the components of the planetesimals making up the terrestrial planets, large amounts of primitive organic precursor molecules are believed to be exogenous in origin and to have been imported to the Earth via micrometeorites, carbonaceous meteorites and comets, especially during the early stages of the formation of the Solar System [1,2]. Our study concerns the hypothesis that prebiotic organic matter, present on Earth, was synthesized in the interstellar environment, and then imported to Earth by meteorites or micrometeorites. We are particularly concerned with the formation and fate of amino acids. We have already shown that amino acid synthesis is possible inside cometary grains under interstellar environment conditions [3]. We are now interested in the effects of space conditions and meteoritic impact on these amino acids [4-6]. Most of the extraterrestrial organic molecules known today have been identified in carbonaceous chondrite meteorites [7]. One of the components of these meteorites is a clay with a composition close to that of saponite, used in our experiments. Two American teams have studied the effects of impact on various amino acids [8,9]. [8] investigated amino acids in saturated solution in water with pressure ranges between 5.1 and 21 GPa and temperature ranges between 412 and 870 K. [9] studied amino acids in solid form associated with and without minerals (Murchison and Allende meteorite extracts) and pressure ranges between 3 and 30 GPa. In these two experiments, the amino acids survived up to 15 GPa. At higher pressure, the quantity of preserved amino acids decreases quickly. Some secondary products such as dipeptides and diketopiperazins were identified in the [8] experiment.

Bertrand, M.↗

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗

Thermal Effects of Pressure Surge and Adiabatic Compression in the Priming of Propulsion and Propellant Transfer Systems

Surge pressures and adiabatic compression during priming of evacuated lines in propulsion and propellant transfer systems has been considered. Test data were obtained for desaturated and saturated water for surge pressures and adiabatic compression for various supply pressures and temperatures. Scaling of surge pressures a t different temperatures has been carried out with the aid of Joukowsky model. The thermal effects associated with surge pressure and the attendant adiabatic compression have been investigated with the a id of a simplified analytical model, which represents an extension of the model developed by Lecourt and Steelant. It has been shown that the predictions from the model compare satisfactorily with test data for a water/helium system, and existing test data for different liquid/gas combinations.

Pressure Surge↗

Stability of polar frosts in spherical bowl-shaped craters on the moon, Mercury, and Mars

A model of spherical bowl-shaped craters is described and applied to the moon, Mercury, and Mars. The maximum temperature of permanently shadowed areas are calculated using estimates of the depth/diameter ratios of typical lunar bowl-shaped craters and assuming a saturated surface in which the craters are completely overlapping. For Mars, two cases are considered: water frost in radiative equilibrium and subliming CO2 frost in vapor equilibrium. Energy budgets and temperatures are used to determine whether a craterlike depression loses mass faster or slower than a flat horizontal surface. This reveals qualitatively whether the frost surface becomes rougher or smoother as it sublimes.

Ingersoll, Andrew P.↗